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# HW02 Answers - Solution for 36217 Wanjie Wang Teacher...

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Solution for 36217 Wanjie Wang Teacher: Jiashun Jin September 15, 2009 Ten points for each problem. If there is any question, please contact me at [email protected] 1.Proof: P ( A B | B ) = P (( A B ) B ) P ( B ) = P ( A B ) P ( B ) = P ( A | B ) 2. The sample space of two dice rolled is Ω = { ( a,b ) | 1 a 6 , 1 b 6 . } . They have equal probability. So, the answers are: P (sum = 2) = 1 / 36 P (sum = 3) = 2 / 36 P (sum = 4) = 3 / 36 P (sum = 5) = 4 / 36 P (sum = 6) = 5 / 36 P (sum = 7) = 6 / 36 P (sum = 8) = 5 / 36 P (sum = 9) = 4 / 36 P (sum = 10) = 3 / 36 P (sum = 11) = 2 / 36 P (sum = 12) = 1 / 36 3. P (at least one dice is6) = P (the ﬁrst dice is six, the second dice is any number) + P (the second dice is six, the ﬁrst dice is any number) - P(both dices are six) = 1 / 6 + 1 / 6 - 1 / 6 * 1 / 6 = 11 / 36 4. According to the results above, the conditional probabilities are: P ( a = 6 | sum = 7) = P ( a sum =7) P ( sum =7) = P (( a,b )=(6 , 1)) P

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HW02 Answers - Solution for 36217 Wanjie Wang Teacher...

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